The weak radiative pion vertex in \tau^- ->\pi^-\nu_\tau l^+ l^- decays

TL;DR

This paper analyzes au^- decays involving a pion, neutrino, and lepton pairs, combining QED and hadronic structure effects to predict branching ratios and spectra, with implications for future experimental measurements.

Contribution

It introduces a model combining Chiral Perturbation Theory and resonance inclusion to accurately evaluate form factors for au^- decays involving lepton pairs.

Findings

Predicted branching ratio for au^- -> u_ au o ext{pion} e^+ e^- decay.

Predicted branching ratio for au^- -> u_ au o ext{pion} \mu^+\mu^- decay.

The first decay mode could be measured soon; the second is less accessible.

Abstract

We carry out a detailed study of the branching fractions and lepton pair invariant-mass spectrum of \tau^- ->\pi^- \nu_\tau l^+l^- decays (l=e,\mu). In addition to the model-independent (QED) contributions, we include the structure-dependent (SD) terms, which encode information on the hadronization of QCD currents. The form factors describing the SD contributions are evaluated by supplementing Chiral Perturbation Theory with the inclusion of the lightest multiplet of spin-one resonances as active degrees of freedom. The Lagrangian couplings have been determined demanding the known QCD short-distance behaviour to the relevant Green functions and associated form factors in the limit where the number of colours goes to infinity. As a result, we predict BR(\tau^- ->\pi^-\nu_\tau e^+e^-)= (1.7^{+1.1}_{-0.3})x10^{-5} and BR(\tau^- -> \pi^-\nu_\tau \mu^+\mu^-) = [0.03,1.0]x10^{-5}. According to this, the first decay could be measured in the near future, which is not granted for the second one.